IDEAS home Printed from https://ideas.repec.org/a/taf/gnstxx/v21y2009i1p19-40.html
   My bibliography  Save this article

Functional linear regression with derivatives

Author

Listed:
  • André Mas
  • Besnik Pumo

Abstract

We introduce a new model of linear regression for random functional inputs taking into account the first-order derivative of the data. We propose an estimation method that comes down to solving a special linear inverse problem. Our procedure tackles the problem through a double and synchronised penalisation. An asymptotic expansion of the mean square prevision error is given. The model and the method are applied to a benchmark dataset of spectrometric curves and compared with other functional models.

Suggested Citation

  • André Mas & Besnik Pumo, 2009. "Functional linear regression with derivatives," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 21(1), pages 19-40.
    • Handle: RePEc:taf:gnstxx:v:21:y:2009:i:1:p:19-40
    DOI: 10.1080/10485250802401046
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/10485250802401046
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/10485250802401046?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Amato, U. & Antoniadis, A. & De Feis, I., 2006. "Dimension reduction in functional regression with applications," Computational Statistics & Data Analysis, Elsevier, vol. 50(9), pages 2422-2446, May.
    2. Brown P.J. & Fearn T & Vannucci M, 2001. "Bayesian Wavelet Regression on Curves With Application to a Spectroscopic Calibration Problem," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 398-408, June.
    3. He, Guozhong & Müller, Hans-Georg & Wang, Jane-Ling, 2003. "Functional canonical analysis for square integrable stochastic processes," Journal of Multivariate Analysis, Elsevier, vol. 85(1), pages 54-77, April.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Hao, Siteng & Lin, Shu-Chin & Wang, Jane-Ling & Zhong, Qixian, 2024. "Dynamic modeling for multivariate functional and longitudinal data," Journal of Econometrics, Elsevier, vol. 239(2).
    2. Hans-Georg Müller & Wenjing Yang, 2010. "Dynamic relations for sparsely sampled Gaussian processes," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(1), pages 1-29, May.
    3. Ahmedou, Aziza & Marion, Jean-Marie & Pumo, Besnik, 2016. "Generalized linear model with functional predictors and their derivatives," Journal of Multivariate Analysis, Elsevier, vol. 146(C), pages 313-324.
    4. Chiou, Jeng-Min & Yang, Ya-Fang & Chen, Yu-Ting, 2016. "Multivariate functional linear regression and prediction," Journal of Multivariate Analysis, Elsevier, vol. 146(C), pages 301-312.
    5. Shang, Han Lin, 2017. "Functional time series forecasting with dynamic updating: An application to intraday particulate matter concentration," Econometrics and Statistics, Elsevier, vol. 1(C), pages 184-200.
    6. Laurent Delsol, 2013. "No effect tests in regression on functional variable and some applications to spectrometric studies," Computational Statistics, Springer, vol. 28(4), pages 1775-1811, August.
    7. Han Shang, 2014. "A survey of functional principal component analysis," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 98(2), pages 121-142, April.
    8. Zhenjie Liang & Futian Weng & Yuanting Ma & Yan Xu & Miao Zhu & Cai Yang, 2022. "Measurement and Analysis of High Frequency Assert Volatility Based on Functional Data Analysis," Mathematics, MDPI, vol. 10(7), pages 1-11, April.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Linjuan Zheng & Beiting Liang & Guochang Wang, 2024. "Adaptive slicing for functional slice inverse regression," Statistical Papers, Springer, vol. 65(5), pages 3261-3284, July.
    2. Chakraborty, Sounak, 2012. "Bayesian multiple response kernel regression model for high dimensional data and its practical applications in near infrared spectroscopy," Computational Statistics & Data Analysis, Elsevier, vol. 56(9), pages 2742-2755.
    3. Fan, Zengyan & Lian, Heng, 2016. "Minimax convergence rates for kernel CCA," Journal of Multivariate Analysis, Elsevier, vol. 150(C), pages 183-190.
    4. Kargin, V. & Onatski, A., 2008. "Curve forecasting by functional autoregression," Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2508-2526, November.
    5. Chakraborty, Sounak & Ghosh, Malay & Mallick, Bani K., 2012. "Bayesian nonlinear regression for large p small n problems," Journal of Multivariate Analysis, Elsevier, vol. 108(C), pages 28-40.
    6. Alvarez, Agustín & Boente, Graciela & Kudraszow, Nadia, 2019. "Robust sieve estimators for functional canonical correlation analysis," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 46-62.
    7. Guochang Wang & Jianjun Zhou & Wuqing Wu & Min Chen, 2017. "Robust functional sliced inverse regression," Statistical Papers, Springer, vol. 58(1), pages 227-245, March.
    8. Ji Yeh Choi & Heungsun Hwang & Michio Yamamoto & Kwanghee Jung & Todd S. Woodward, 2017. "A Unified Approach to Functional Principal Component Analysis and Functional Multiple-Set Canonical Correlation," Psychometrika, Springer;The Psychometric Society, vol. 82(2), pages 427-441, June.
    9. Ciarleglio, Adam & Todd Ogden, R., 2016. "Wavelet-based scalar-on-function finite mixture regression models," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 86-96.
    10. Ross Iaci & T.N. Sriram & Xiangrong Yin, 2010. "Multivariate Association and Dimension Reduction: A Generalization of Canonical Correlation Analysis," Biometrics, The International Biometric Society, vol. 66(4), pages 1107-1118, December.
    11. Wang, Qin & Yao, Weixin, 2012. "An adaptive estimation of MAVE," Journal of Multivariate Analysis, Elsevier, vol. 104(1), pages 88-100, February.
    12. Manteiga, Wenceslao Gonzalez & Vieu, Philippe, 2007. "Statistics for Functional Data," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 4788-4792, June.
    13. Wang, Guochang & Lin, Nan & Zhang, Baoxue, 2013. "Functional contour regression," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 1-13.
    14. Ruzong Fan & Hong-Bin Fang, 2022. "Stochastic functional linear models and Malliavin calculus," Computational Statistics, Springer, vol. 37(2), pages 591-611, April.
    15. Benhenni, Karim & Hassan, Ali Hajj & Su, Yingcai, 2019. "Local polynomial estimation of regression operators from functional data with correlated errors," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 80-94.
    16. Mariano J. Valderrama & Francisco A. Ocaña & Ana M. Aguilera & Francisco M. Ocaña-Peinado, 2010. "Forecasting Pollen Concentration by a Two-Step Functional Model," Biometrics, The International Biometric Society, vol. 66(2), pages 578-585, June.
    17. Pian Chen & Aaron Smith, 2013. "The nonlinear multidimensional relationship between stock returns and the macroeconomy," Applied Economics, Taylor & Francis Journals, vol. 45(35), pages 4985-4999, December.
    18. R. G. Aykroyd & K. V. Mardia, 2003. "A wavelet approach to shape analysis for spinal curves," Journal of Applied Statistics, Taylor & Francis Journals, vol. 30(6), pages 605-623.
    19. Guochang Wang & Xiang-Nan Feng & Min Chen, 2016. "Functional Partial Linear Single-index Model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(1), pages 261-274, March.
    20. Paulo M. M. Rodrigues & Mirjam Salish & Nazarii Salish, 2024. "Saving for sunny days: The impact of climate (change) on consumer prices in the euro area," Papers 2401.03740, arXiv.org.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:taf:gnstxx:v:21:y:2009:i:1:p:19-40. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/GNST20 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.